Determining the area of a ring (also known as an annulus) is straightforward if you know the outer radius and the inner area. Follow this guide for an easy calculation.
Step 1: Understand the Formula
To find the area of the ring, you will use the given outer radius and inner area. The formulas involved are:
\[ \text{Area of Ring} = \pi R^2 - \text{Inner Area} \]
where:
- \( R \) is the outer radius
- \( \pi \) (Pi) is approximately 3.14159
Step 2: Use Real Numbers for Calculation
Suppose the outer radius (\( R \)) is 12 units and the inner area is 50.265 square units.
Step 3: Calculate the Area of the Outer Circle
First, calculate the area of the outer circle using the formula \( \pi R^2 \):
\[ \text{Area of Outer Circle} = \pi \times R^2 \]
\[ \text{Area of Outer Circle} = \pi \times 12^2 \]
\[ \text{Area of Outer Circle} = \pi \times 144 \]
\[ \text{Area of Outer Circle} = 3.14159 \times 144 \]
\[ \text{Area of Outer Circle} = 452.389 \, \text{square units} \]
Step 4: Calculate the Area of the Ring
Next, subtract the inner area from the outer area to find the area of the ring:
\[ \text{Area of Ring} = \text{Area of Outer Circle} - \text{Inner Area} \]
\[ \text{Area of Ring} = 452.389 - 50.265 \]
\[ \text{Area of Ring} = 402.124 \, \text{square units} \]
So, the area of the ring is 402.124 square units.
Summary
To summarize, the steps to calculate the area of a ring when the outer radius and inner area are known are:
1. Calculate the area of the outer circle using the formula \( \pi R^2 \).
2. Subtract the inner area from the outer area.
Using our example, with an outer radius of 12 units and an inner area of 50.265 square units, we found the area of the ring to be 402.124 square units.
By following these steps, you can easily calculate the area of a ring for any given outer radius and inner area.
